Numerical estimation of the piecewise constant Robin coefficient by identifying its discontinuous points

作者：Cheng Xiao-liang^*; Yu Yuan-jie

来源：Applied Mathematics. Series B, A Journal of Chinese Universities, 2015, 30(1): 1-16.

DOI：10.1007/s11766-015-3197-7

• Inverse problem
• Robin coefficient
• differentiability
• the Gauss-Newton method

We propose a new numerical method for estimating the piecewise constant Robin coefficient in two-dimensional elliptic equation from boundary measurements. The Robin inverse problem is recast into a minimization of an output least-square formulation. A technique based on determining the discontinuous points of the unknown coefficient is suggested, and we investigate the differentiability of the solution and the objective functional with respect to the discontinuous points. Then we apply the Gauss-Newton method for reconstructing the shape of the unknown Robin coefficient. Numerical examples illustrate its efficiency and stability.

• 出版日期2015-3
• 单位浙江大学